Algorithm to get IN and OUT component of a directed graph

[salfaris]

I have added functions to extract the IN and OUT components of a directed graph (that contains a strongly connected component) using a simple random-start BFS. The IN and OUT components are those as described in this paper by Broder et al.

This is my first PR in NetworkX, so I apologize beforehand if my code is badly written. In particular, I was having a lot of thoughts on how to properly refactor the in_component and out_component as their code content share a lot of similar lines. I look forward to hearing from the community on how to do this correctly as I am here to learn.

Some future work that I am considering are:

1. Add more tests.
2. Algorithm to compute TENDRILS and TUBE (refer to Broder et al.).
3. Uniting these components under a single Bow-tie diagram (defined by these IN, OUT, TENDRILS, TUBE components) function.

[rossbar]

I may be misunderstanding something, so please correct me where I'm wrong!

From the paper, the definition of the IN component is "the set of nodes that can reach the SCC but can't be reached by it". This sounds like it's directly translatable to NX without the need for extra machinery like random and bfs. For example, assuming you have a DiGraph G and a set of nodes scc corresponding to the strongly-connected component of interest:

>>> others = G.nodes() - scc
>>> in_component = frozenset(
...     u for u in others if set(G.successors(u)) & scc and not
...     set(G.predecessors(u)) & scc
... )

Out-component then follows the same pattern, but with predecessors and successors switched.

Assuming I've understood correctly, I would argue that it's straightforward to construct the in and out components this way and so adding dedicated functions to do so would be unnecessary.

[rossbar]

This one has been stale for quite awhile so I will go ahead and close it. @salfaris if you're interested in picking this up again, please feel free to do so - the last comment re: a (proposed) simpler way of producing the components would be a good starting point to re-kindle the discussion!